We divide 37635 by 45
We're looking to find how many times 45 goes into 37635.

Moving on to step 1:
45 goes into 3 0 times with a remainder of 3.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
If we take 0 away from 3, we end up with 3.
Take the next digit (7) from the dividend and append it to 3, then repeat: 37 / 45

Going ahead to step 2:
45 goes into 37 0 times with a remainder of 37.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
Deduct 0 from 37 and we're left with 37.
Take the next digit (6) from the dividend and append it to 37, then repeat: 376 / 45

Step 3:
When dividing 376 by 45, we get 8 with a remainder of 16.
Record the quotient 8 as the next digit in the result. 
Result so far: 8.0
If we subtract 360 from 376, we get 16.
Include the next digit (3) from the dividend after 16, then repeat: 163 / 45

Let's proceed to step 4:
If we divide 163 by 45, we get 3 and a remainder of 28.
Record the quotient 3 as the next digit in the result. 
Result so far: 83.0
If we take 135 away from 163, we end up with 28.
Grab the next digit (5) from the dividend, add it to 28, then carry on: 285 / 45

Let's proceed to step 5:
If we divide 285 by 45, we get 6 and a remainder of 15.
Write down 6 as next digit of the result. 
Result so far: 836.0
If we take 270 away from 285, we end up with 15.
Since there are no more digits in the dividend, we add a zero to the remainder making it 150, and continue the process.

Let's proceed to step 6:
If we divide 150 by 45, we get 3 and a remainder of 15.
Record the quotient 3 as the next digit in the result. 
Result so far: 836.3
The remainder is 15 after subtracting 135 from 150.
Since there are no more digits in the dividend, we add a zero to the remainder making it 150, and continue the process.

Advancing to step 7:
When dividing 150 by 45, we get 3 with a remainder of 15.
Use 3 as the next digit of our solution. 
Result so far: 836.33
If we subtract 135 from 150, we get 15.
Since there are no more digits in the dividend, we add a zero to the remainder making it 150, and continue the process.

The quotient of the division is 836.33, and the remainder is 0.015.